You are using Email to Case Premium and notice that an Auto-Response email is being sent despite the rule criteria for your Auto-Response rule not being met. When sending emails via standard standard Email-to-Case, an Auto-Response email is not sent as you expected.

According to Salesforce's documentation on Auto-Response rules, if none of the rule entries under your Case Auto-Response rule are met, Salesforce will default to sending the Default Response Template defined under your Web-to-Case settings (if a template is specified).

Email to Case Premium currently respects this documented behavior.

For an unknown reason, standard Email-to-Case does not. In the event Case Auto-Response rule entries are not met (when using standard Email-to-Case), the Default Response Template defined under Web-to-Case will NOT be used.

For further assistance in regards to issues with Case Auto-Response rules, please see the following knowledge article.